1. Field of the Invention
The present invention relates to filters used for electric circuits in radio equipment, etc. or transmission lines, and more particularly to micromachine vibration filters which provide sharp selectivity through micromechanical vibration, in highly integrated circuits for handling signals in the MHz to GHz range.
2. Description of the Related Art
FIG. 1 shows a conventional mechanical vibration filter in a simplified form (see IEEE Journal of Solid-state Circuits, Vol. 35, No. 4, pp. 512 to 526, April 2000). This filter consists of a thin-film coated silicon substrate which bears an input waveguide 104 and an output waveguide 105, beam resonators 101 and 102 which are fixed at each end with gaps of one micrometer or less from the waveguides, and a coupling beam 103 connecting the two beams. A signal entering through the input waveguide 104 is capacitively coupled with the resonator 101, which generates static electricity. Mechanical vibration occurs only when the frequency of the signal approximately coincides with the resonance frequency of an elastic structure composed of the resonators 101 and 102 and the coupling beam 103. Hence, this mechanical vibration is detected as a capacitance variation between the output waveguide 105 and the resonator 102 so that the input signal is thus filtered and picked up as an output signal.
For a doubly-supported beam with a rectangular cross section, its resonance frequency f is expressed by the following formula:                     f        =                  1.03          ⁢                      t                          L              2                                ⁢                                    E              ρ                                                          (        1        )            
where E represents elasticity modulus, ρ density, t thickness, and L length.
According to the formula, if the beam material is polysilicon, E=160 Gpa, ρ=2.2×103 kg/m3, L=40 μm, t=1.5 μm, then f=8.2 MHz. Therefore it is possible to make a band-pass filter with a center frequency of approximately 8 MHz. As compared with a filter based on a passive circuit having a capacitor and a coil, the filter thus structured provides high Q factor and sharp frequency selectivity.
As apparent from Formula 1, in order to make a high frequency band filter, the first thing to do is to increase the value of E/ρ by changing the material. However, when E is larger, the amount of beam displacement is smaller even if the force to deflect the beam is the same, and thus it is difficult to detect the amount of beam displacement. When a static load is applied to the surface of a doubly-supported beam and d represents the amount of deflection of the center of the beam and L the length of the beam, the beam flexibility is expressed as d/L and the following proportionality relation of d/L as indicated by Formula 2 exists:                               d          L                ∝                                            L              3                                      t              3                                ·                      1            E                                              (        2        )            
Hence, in order to increase the resonance frequency while maintaining the value of d/L constant, a material whose density ρ is low should be used because E cannot be increased. It is thus necessary to use a low-density material whose Young's modulus is equivalent to that of polysilicon. Therefore, a composite material such as CFRP (Carbon Fiber Reinforced Plastics) should be used. In this case, it is difficult to make a micromachine vibration filter through the semiconductor manufacturing process.
An alternative approach which does not use such a composite material is to change the beam size to increase the value of t·L−2 in Formula 1. However, if t is increased and L is decreased, the value of d/L in Formula 2 as a beam flexibility indicator decreases, which means that it becomes more difficult to detect the amount of beam deflection.
Next is an explanation of the relation between log L and log t in Formulas 1 and 2. FIG. 2 is a characteristic graph showing the relation between the size of a typical mechanical vibration filter and frequency. In the graph, the line with gradient 2 illustrates the relation between log L and log t in Formula 1, and the line with gradient 1 illustrates the relation between log L and log t in Formula 2. In the graph (FIG. 2), assuming point A (which denotes the current size) as the start point, when L and t are above the gradient 2 line, the value of f increases; and on the other hand, when L and t are below the gradient 1 line, the value of d/L increases. Hence, when L and t are within the hatched region of the graph, the resonance frequency is increased while the amount of beam deflection is maintained. As FIG. 2 indicates, in order to make a high frequency mechanical vibration filter, it is necessary for both L and t to be very small. It is a sufficient condition to decrease L and t at the same scaling factor, namely decrease L and t along the gradient 1 line in order to assure that L and t fall within the hatched region of the graph (FIG. 2).
As discussed above, the use of very small micromechanical vibrators increases the resonance frequency. However, for example, in a mechanical vibration filter as shown in FIG. 1, this necessitates the input and output waveguides to come closer to each other, which might cause direct coupling of the input waveguide's electromagnetic field. This might result in leakage of an unwanted band signal, leading to superimposed noise in the output waveguide. Also, since the amplitude of beam vibration decreases, the signal which detects the vibration is weak and susceptible to disturbance.